There has been proposed a laser light generating apparatus in which a nonlinear optical crystal device is disposed in a resonator. The nonlinear optical crystal device converts a wavelength of a fundamental wave laser light incident therein efficiently by utilizing a high power density in the resonator.
There has been proposed two kinds of laser light generating apparatus. A laser light generating apparatus has a wavelength converting device disposed in a resonator. A nonlinear optical crystal device such as an SHG (second harmonic generation) device is used as a wavelength converting device. This laser light generating apparatus is called "external resonator SHG apparatus". In this case, a fundamental wave light source is not located in the resonator. Another laser light generating apparatus has a wavelength converting device and a fundamental wave light source located in a resonator. This laser light generating apparatus is usually used as a fundamental wave light source for the external resonator SHG apparatus.
The SHG apparatus of external resonator type is explained as follows. A nonlinear optical crystal device is disposed between a pair of reflection mirrors composing an external resonator thereof. A fundamental wave laser light is incident on the external resonator and passed through the nonlinear optical crystal device. The resonator length of the external resonator is selected to resonate with a frequency (wavelength) of incident laser light.
The SHG apparatus of external resonator type increases a so-called finesse value (which corresponds to a Q value of resonance) of the resonator to a value ranging from 100 to 1000. The increase of the finesse value increase an optical density in the resonator several hundred times as much as an optical density of incident light. Therefore a nonlinear effect of the nonlinear optical crystal device in the resonator becomes efficient.
As a light source of the fundamental wave laser light for the SHG apparatus of external resonator type, there can be used the laser light generating apparatus in which a laser medium and a nonlinear optical crystal device are disposed between a pair of reflection means composing the laser resonator. Here, a SHG device can be used as a nonlinear optical crystal device. In this case, the laser light generated by radiating a pumping light on the laser medium in the laser resonator is supplied as the fundamental wave to the nonlinear optical crystal device disposed in the resonator. The fundamental wave laser light is converted to a higher harmonic wave laser light. The harmonic wave laser light is made incident on the above external resonator, and then made incident on the nonlinear optical crystal device in the external resonator.
As described above, in the laser light generating apparatus which obtains a laser light of a second harmonic wave or a laser light, such as a higher harmonic wave, a sum frequency wave or the like through wavelength conversion, a change (error) of an optical path in the external resonator should be set to a range from 1/1000 to 1/10,000 of the resonator length. In particular, a position of the external resonator should be controlled within an extremely high accuracy such as 1 Angstrom (.ANG.) or smaller.
Therefore, there has been proposed a method wherein the resonator length can be automatically controlled to stabilize the resonance operation for the incident laser light on the external resonator. In this method, the reflection means composing the resonator are movable, which can be moved by the actuator minutely in the optical axis direction. A servo loop is constructed, in which an error signal in proportion to difference of the resonator length with respect to the laser light incident on the resonator is fed back to the actuator.
One of the methods for obtaining the error signal is a Drever Locking (Drever Locking) method in which the fundamental wave laser light is frequency-modulated (FM) or phase-modulated (PM) with a constant frequency. Then intensity and phase of reflected light from the external resonator are detected to thereby obtain the error signal with high accuracy (see R. W. P. Drever et al. "Laser Phase and Frequency Stabilization Using an Optical Resonator", Applied Physics B 31. 97-105 (1983)).
A principle of detecting the error signal thereof will be described briefly which is disclosed in Japanese Laid-open Patent Publication No. 5-243661.
When the SHG device having a refractive index n and a thickness T is disposed in the Fabry-Perot resonator, various constants are defined as follows:
T: transmittance obtained when the light is traveled in the single optical path PA1 .eta.: SHG conversion efficiency of the SHG device obtained when the light is traveled in the single optical path PA1 R.sub.1 : reflectivity of incidence plane PA1 R.sub.2 : reflectivity of reflection plane
Here, a reflectivity R.sub.m upon reflection plane including a loss caused by a round-trip travel of the light in the resonator is given by the following Equation (1). A complex reflectivity r of the light reflected by the resonator is represented by the following Equation (2). ##EQU1##
A reflected light intensity .vertline.r.vertline..sup.2 and its phase at this time are shown in FIGS. 7 and 8, respectively. Side bands (fc.+-.fm) relative to the frequency fc of the laser light incident on the resonator are set by a phase modulator of a frequency fm. A beat between the frequency fc and the frequencies (fc.+-.fm) of returning light from the resonator of a resonating frequency f.sub.0 is detected, thereby obtaining the error signal having polarity.
Here, if a modulation index in the phase modulation is represented by a symbol .beta. and an electric field of a fundamental light source is represented by Equation of E=E.sub.0 e.sup.jwct, the electric field obtained after modulation is given by Equation (3). EQU E=E.sub.0 exp [j.omega..sub.c t+.beta. sin .omega..sub.m t](3) EQU (.omega..sub.c =2.pi.f.sub.c, .omega..sub.m =2.pi.f.sub.m)
If this Equation (3) is developed by using Bessel function, Equation (4) is obtained. ##EQU2##
In Equation (4), when the modulation index .beta. is smaller than 0.2, terms of J.sub.2 (.beta.) or higher can be disregarded in Equation 4. Therefore it is substantially sufficient to consider only the value .omega..sub.c and the two side bands (.omega..sub.c .+-..omega..sub.m). Accordingly, the electric field E can be represented by the following Equation 5. EQU E=E.sub.0 (J.sub.0 (.beta.) exp [j.omega..sub.c t]+J.sub.1 (.beta.){exp [j(.omega..sub.c +.omega..sub.m)t]-exp [j(.omega..sub.c -.omega..sub.m)t]}(5)
The complex reflectivity is calculated in each term of the Equation (5) so that the electric field of the reflected light from the resonator is represented by Equation (6). ##EQU3## where ##EQU4## Here, since .beta. is smaller than 0.2, the values of J.sub.0 (.beta.) and J.sub.1 (.beta.) can be made approximate as ##EQU5## If the above values are substituted in Equation (6) and terms having a value .beta. of second degree or higher are disregarded, then the intensity .vertline.E.vertline..sup.2 of the reflected light can be represented by Equation (7). ##EQU6##
A DC component of a detected signal of the intensity of the reflected light is cut and the signal is multiplied with a value sin .omega.t obtained by applying a proper phase to an original modulated signal. When a component of a wave (2.omega..sub.m) having twice frequency is removed from the signal by a low-pass filter, only the term of .beta. E.sub.0.sup.2 I.sub.m [r(.DELTA..sub.c)*(.DELTA..sub.c+m)+r(.DELTA..sub.c)*(.DELTA..sub.c-m)] can be obtained. This term is set as a resonator-length error signal. Then, a servo for locking the resonator length can be effected, using the resonator-length error signal.
Specifically, as shown by a solid curve in FIG. 3A, the intensity of the reflected light from the resonator indicates a minimum value (dark light) in a resonating state of the resonator and indicates a high level (bright light) in a non-resonating (non-matched) state. The resonator error signal obtained as described above is obtained as a signal shown by a solid line in FIG. 3B. The cavity length servo is effected when the signal crosses an intensity level of 0.
However, in this case, the intensity of the reflected light from the resonator is discrete as shown in FIG. 9. Therefore, the error signal obtained only when the resonator is brought in its resonating state is discrete so that the error signal cannot constantly be obtained. Further, as shown in FIG. 3, a region A where the error signal can be obtained is considerably narrow so that a width of the region A is at most several tens .ANG., about 6 .ANG., for example, obtained by conversion into the resonator length. However, an interval of the error signal is 1000 times as wide as the region A, so that it is difficult to reliably set the resonator length into its locked state.